Substitution Effects of Diborane on the Interaction with Borazine

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Substitution Effects of Diborane on the Interaction with Borazine (Inorganic Benzene) P. Ravinder and V. Subramanian* Chemical Laboratory, Central Leather Research Institute, Council of Scientific and Industrial Research, Adyar, Chennai 600 020, India ReceiVed: NoVember 11, 2009; ReVised Manuscript ReceiVed: March 22, 2010

The gas phase interaction between borazine (IBz) and diborane (DB) has been investigated using MP2/6311++G** and M05-2X/6-311++G** methods. The calculations have also been carried out at the same levels on the intermolecular complex formed between benzene (Bz) and DB to compare the modes of interaction. The complexation pattern found in IBz · · · DB is similar to that of Bz · · · DB due to their structural similarity. The calculated stabilization energies (SEs) at the MP2/6-311++G** level of theory for IBz · · · DB and Bz · · · DB complexes are 1.67 and 3.06 kcal/mol, respectively. The corresponding values obtained from the M05-2X/6-311++G** level of calculation are 2.55 and 3.43 kcal/mol. The variation in the SEs between IBz · · · DB and Bz · · · DB is due to the differences in the π-electron distributions of IBz and Bz rings. Since, DB contains a three center-two electron (3c-2e) electron deficient bond, the substitution of nonbridge hydrogen atoms (H) by different functional groups may influence the nature of interaction between the DB and IBz. Thus, the nonbridge H atom in DB has been substituted by electron withdrawing (CN and Cl) and electron donating (CH3) groups. The interaction between substituted DBs and IBz has also been investigated using CCSD(T), MP2, and M05-2X methods. Results reveal that the substitution of the nonbridge H atom of DB by a cyano group significantly influences the calculated stabilization energies (SEs) and geometrical parameters whereas substitution by Cl and CH3 groups marginally affects the stabilities and geometrical parameters of the substituted complexes. The calculated SEs of various substituted DB and IBz complexes range from 1.87 to 7.91 kcal/mol. Furthermore, evidence shows that SEs vary linearly with the number of substituents present in the complexes. The energy decomposition analysis using the density functional theorysymmetry adopted perturbation theory (DFT-SAPT) method confirms the predominant role played by the dispersion interaction in the stabilization of the various complexes when compared to the electrostatic interaction. Introduction Numerous attempts have been made to classify the hydrogen bonding (H-bonding) interaction based on energetics and geometrical and spectral parameters.1 The H-bonding strength ranges from van der Waals to the covalent limit.2 Although the H-bonding interaction can be classified as strong, moderate (conventional), and weak on the basis of the above-mentioned parameters, the borderless nature of the hydrogen bonding interaction has been highlighted.2b,3 Desiraju et al. have introduced the concept of a “Hydrogen Bridge” to unify all of the nonbonded interactions in which hydrogen atom acts as a bridge between any two atoms.2b It is evident from previous studies that the electrostatic interaction plays a major role in the strong and moderate H-bonded systems.1c,2b,3b,4 In the case of weak H-bonded systems, dispersive interaction contributes significantly to the strength rather than the electrostatic. As the strength of the interaction increases from the weak limit, the electrostatic interaction increases and becomes increasingly covalent with increasing strength.2,3 It is evident from the conventional definition of H-bonding that the formation of the X-H · · · Y bond is accompanied by a weakening of the covalent X-H bond with a concomitant decrease of the X-H stretching frequency (red shift).5 This red shift belongs to one of the most important characteristics of the H-bonding interactions.5 Its other signature has considerable increase in the intensity of the spectral band * To whom correspondence should be addressed. Tel.: +91 44 24411630. Fax: +91 44 24911589. E-mail: [email protected].

connected with the X-H stretching frequency.5 In addition, there is a small amount of transfer of electron density from the proton acceptor (lone pair) to the σ*-antibonding orbital of the X-H moiety, which causes a weakening of this bond and a decrease in the X-H stretching frequency.5 On the contrary, there are some typical situations, wherein the X-H bond gets compressed and the corresponding X-H stretching vibration is shifted to a high frequency. This type is called blue shifting improper or anti-H-bonding.5a Recently, various situations in which Hbonded systems exhibit red, blue, and no shifts have been systematically analyzed.5 In the characterization of different types of H-bonding interaction, the usefulness of natural bond orbital analysis (NBO) and the theory of atoms in molecules (AIM) have been demonstrated in previous studies.6 In the assessment of weak H-bonding interaction, various model systems have been selected. In this category, diborane (DB) has been used as one of the model systems by researchers due to the discovery of an interaction between n-B18H22 and benzene (Bz) in the molecular crystal in which the bridging H atom of n-B18H22 directly interacts with the center of the benzene.7 To understand the nature of interaction between the boron hydride and benzene, studies have been undertaken to model the interaction between the DB and π-systems.8 Also, it is interesting to probe the interaction between the electron-poor boron hydride with the electron rich π-systems. Furthermore, DB is intensively studied molecule in inorganic chemistry due to its three center-two electron (3c-2e) τ-bond.9 The strength of the Bz · · · DB complex is 3.27 kcal/mol at the MP2/6-

10.1021/jp910717j  2010 American Chemical Society Published on Web 04/08/2010

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SCHEME 1: Description of the Mode of Interaction Between IBz and DB with Atomic Numbering

TABLE 1: Calculated Geometrical Parameters and Stabilization Energies (SEs) for Bz · · · DB and IBz · · · DB Complexesa parameters d R (B-H1) R (B-H2) A (B-H1-B) A (B-H2-B) SEMP2/6-311++G** SEM05-2X/6-311++G** SEM05-2X/6-311+G**

Bz · · · DB complex 2.419(2.413) 1.313(1.314) 1.318(1.319) 84.28(84.34) 83.88(83.91) 3.06(3.27) 3.43 3.43

IBz · · · DB complex 2.545 1.316 1.321 83.65 83.24 1.67 2.55 2.57

a Values in the parentheses are taken from ref 8b d and R are in Å, A are in degrees, and SE are in kcal/mol.

311++G** level of theory.8b Evidence from the previous study reveals that the dispersive interaction predominantly stabilizes the formation of this intermolecular complex.8b Similar to DB, borazine (IBz) is popularly known as inorganic benzene and it is another fascinating molecule in chemistry.9 It is isostructural and isoelectronic with Bz.9 As prompted by the earlier study on the Bz · · · DB complex, it is interesting to investigate how DB interacts with the IBz and to explore how substitutions on the DB influence the interaction between the DB and IBz. Various quantum chemical methods used to investigate noncovalent interactions in molecular systems have been reviewed.10 The usefulness of Møller-Plesset second-order perturbation (MP2) and coupled cluster theory with single, double, and triple excitation CCSD(T) methods employing

Ravinder and Subramanian various basis sets have been illustrated.11 The CCSD(T) method is computationally feasible for exploring noncovalent interactions in a molecular system that consists of ∼10 atoms.12 Currently, molecular systems having ∼100 atoms can be handled using the MP2 method.12 The failure of the most popular density functional theory (DFT) based Becke’s three-parameter hybrid exchange functional and Lee-Yang-Parr correlation functional (B3LYP) method in delineating the weak interaction (dispersive nature) in various systems has also been reported.13 Hence, initiatives have been undertaken to develop new exchange and correlation functionals to enhance the quality of prediction and expand the applicability of DFT methods to probe weak interactions.14 Scuseria and Staroverov have reviewed the various strategies used to refine various density functionals.15 Truhlar and co-workers have made significant contributions to the development of functionals with wide applicability in chemistry using diverse set of training and test sets.14 It has been illustrated in previous studies that the M05-2X functional yields reliable results for noncovalent interactions within 5 Å.14c The performance of M05-2X has been attributed to the parameters obtained from the simultaneous optimization of exchange and correlation functionals including kinetic energy density.14 Hence, both MP2 and M05-2X methods are attractive approaches in addition to the other new DFT methods such as M06 and M06-2X.12,14 Therefore, in this study, a systematic attempt has been made to probe the interaction between DB and IBz using MP2 theory and the M05-2X method employing 6-311+G** and 6-311++G** basis sets. Comparison of the trends obtained from the MP2 and M05-2X methods with CCSD(T) employing the 6-31G* basis set has also been carried out. Both the NBO and AIM analysis tools have been applied to characterize the nature of the interaction in the various intermolecular complexes. To understand the interplay of dispersion and electrostatic interactions in the stabilization of various intermolecular complexes, DFT-SAPT analysis has also been performed. Computational Details The geometries of all the complexes were optimized without any constraints using the MP2 method employing 6-31G* and 6-311++G** basis sets. The harmonic vibrational frequency calculations were carried out at the MP2/6-31G* level. The characteristic zero imaginary frequency criterion was satisfied for all the complexes, which ensures that the geometries are minima on their respective potential energy surfaces. Owing to the nature of the nonbridge hydrogen atoms, mono-, di-, tri-,

Figure 1. Optimized geometries of complexes IBz · · · DB and Bz · · · DB with important bond lengths (in Å) at various level of calculations. Red, black, and blue numbers represent the values calculated from MP2/6-311++G**, M05-2X/6-311++G**, and M05-2X/6-311+G** methods, respectively.

Interaction between Borazine and Diborane

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Figure 2. Molecular electrostatic potential isosurfaces (0.0094 au) of IBz, Bz, IBz · · · DB, and Bz · · · DB complexes.

Figure 3. Molecular graphs of IBz · · · DB and Bz · · · DB complexes.

and tetrasubstituted derivatives of DB are possible. Thus CN, Cl, and CH3 groups were used to substitute the nonbridge hydrogen atoms. Since these groups exhibit different electron withdrawing/donating nature, the role of these substitutions in the stabilization of the intermolecular complexes was also assessed. Scheme 1 shows the mode of interaction between the IBz and DB along with relevant atom numbering. It can be seen from the scheme 1 that the distance between the H1 atom of the DB and the center of the π-ring is denoted as d. This parameter was used to characterize the strength of the interaction. The strength of the H-bonding interaction was calculated using the supermolecular approach. The stabilization energy (SE) of the complex is defined as

SE ) -(Ecomp -

∑

Emonomer)

(1)

monomer

where Ecomp and Emonomer are the energies of the complexes and monomers, respectively. The energies of the monomers were calculated from the respective monomer geometries in the complexes, or in other words, the energy that results from complexation was taken into account. The calculated SEs were corrected for basis set superposition error using the counterpoise method suggested by Boys and Bernardi.16 Both geometry optimization and SE calculations were also performed using the M05-2X level of theory employing 6-311+G** and 6-311++G** basis sets. The NBO charges were used to understand the role of electrostatic interaction in the formation of weak complexes. Furthermore, to compare the trends obtained from MP2 and M05-2X methods, single point calculations were performed for

MP2/6-311++G**geometries using CCSD(T)/6-31G* level. Due to the computational demand of the CCSD(T) method, we could not carry out calculations using larger basis sets.12 All the calculations were performed using the Gaussian 03 suite of packages.17 The wave functions obtained from HF/6311++G** were considered in scrutinizing the electron density topographical features of various complexes using Bader’s theory of atoms in molecule employing AIM 2000 software package.18 Energy decomposition analysis has received widespread attention due to its usefulness in understanding the nature of the interaction.19 In this study, the DFT-SAPT methodology was used to gain insight into the nature of the predominant interaction involved in the stabilization of various complexes. DFT-SAPT uses monomer properties and electronic densities from the DFT calculation to compute the interaction energies using symmetry adapted perturbation theory (SAPT).20 This method determines the total interaction energy as a sum of physically meaningful contributions, such as those arising from electrostatics, dispersion, induction, and exchange.21 Various contributions are defined in eq 2. 1 Electrostatic contribution: Eelec ) Epol

(2a)

2 2 Induction contribution: Eind ) Eind + Eex-ind

(2b)

2 2 Dispersion contribution: Edis ) Edis + Eex-dis

(2c)

Exchange contribution: Eexch ) E1ex

(2d)

1 2 2 1 2 2 , Eind , Edis , Eex , Eex-ind , and Eex-dis are first-order where Epol electrostatic, second-order induction, second-order dispersion energies, first-order exchange, second-order exchange-induction, and second-order exchange-dispersion energies, respectively. All these calculations were carried out using LPBE0AC potential employing cc-pVQZ basis set with the help of Molpro (Version 2009.1) suit of program.22

Results and Discussion The calculated BSSE corrected stabilization energies (SEs) and geometrical parameters for IBz · · · DB and Bz · · · DB complexes are presented in Table 1. The optimized geometries of complexes are depicted in Figure 1. The calculated SEs at the MP2/6-311++G** level for the Bz · · · DB and IBz · · · DB complexes are 3.06 and 1.67 kcal/mol, respectively. The d values for Bz · · · DB and IBz · · · DB complexes are 2.419 and 2.545 Å, respectively. The calculated SE values from M05-2X/6311+G** and M05-2X/6-311++G** levels for the Bz · · · DB complex are 3.43 and 3.43 kcal/mol, respectively. The same protocols yield 2.57 and 2.55 kcal/mol for the IBz · · · DB complex. It is possible to note that SE values calculated using the M05-2X method is considerably higher than MP2 results due to the inherent parametrization of M05-2X method.14c It can be seen that there are no significant differences in the geometry of DB in the two complexes and also when compared to the geometry of the free monomer. However, the calculated d values are appreciably dissimilar. The variations in the geometrical parameters and SEs are due to the difference in the inherent π-electron density distribution of Bz and IBz. The presence of an electron deficient boron atom in the IBz ring significantly alters the π-electron cloud of the ring. Due to the

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Figure 4. Optimized geometries of various complexes (DB containing various numbers of electron withdrawing groups) selected in the present study with their corresponding bond lengths (in Å). Red, black, and blue numbers represent the values calculated from MP2/6-311++G**, M052X/6-311++G**, and M05-2X/6-311+G** methods, respectively. [Here 1 and 2 correspond to CN and Cl substitution and a, b, c, d, and e represent mono, 1,2-cis, 1,2-trans, tri, and tetra substitutions in each category.]

electronegativity difference between the boron and nitrogen atoms, charge localization is more on the nitrogen atom. As a result, the π-electron distribution in IBz is “lumpy” when compared to Bz. With a view to assess the differences in the π-electron distribution, the molecular electrostatic potential of Bz and IBz have been calculated using the geometries obtained from the MP2/6-311++G** level of computation. The MESP features of Bz and IBz are shown in Figure 2. The disparity in the π-electron distribution between IBz and Bz are clearly evident from the MESP isosurfaces. Figure 3 illustrates the AIM topography of Bz · · · DB and IBz · · · DB complexes. Although the overall electron density topographies of these two weak H-bonded complexes are alike, there are noticeable variations in the bond paths and the number

of bond critical points (BCPs). The value of electron density and its Laplacian at BCP are denoted as F(r) and 32F(r). The bond paths connecting the H1 of DB with the IBz ring are denoted as b1, b2, and b3, respectively. The bond paths between the H1 of DB and Bz are referred to as b1 and b2. The calculated values of F(r) at the BCPs in b1, b2, and b3 are 0.0067, 0.0067, and 0.0049 au, respectively. The corresponding 32F(r) values are 0.0051, 0.0051, and 0.0043 au. In the case of Bz · · · DB, the F(r) values noticed at (BCPs) b1 and b2 are 0.0059 and 0.0059 au, respectively. The corresponding 32F(r) are identified as 0.0204 and 0.0204 au. These results emphasize that the nature of weak interaction in the IBz · · · DB is similar to that in the Bz · · · DB complex.

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TABLE 2: Calculated SE Values for Different Complexes at MP2 and M05-2X Levels of Theories SE (kcal/mol) MP2

M05-2X

complex

1a

1a

2b

SE/sub (kcal/mol)

IBz · · · DB IBz · · · mono-CN-DB IBz · · · cis-di-CN-DB IBz · · · trans-di-CN-DB IBz · · · tri-CN-DB IBz · · · tetra-CN-DB IBz · · · mono-Cl-DB IBz · · · Cis-di-Cl-DB IBz · · · trans-di-Cl-DB IBz · · · tri-Cl-DB IBz · · · tetra-Cl-DB IBz · · · mono-Me-DB IBz · · · cis-di-Me-DB IBz · · · trans-di-Me-DB IBz · · · tri-Me-DB IBz · · · tetra-Me-DB

1.67 3.31 4.47 4.64 6.30 7.91 2.18 2.64 2.57 2.94 3.23 1.87 2.05 2.03 2.25 2.56

2.55 4.31 5.66 5.88 7.71 9.34 3.47 4.32 4.42 5.14 5.91

2.57 4.32 5.68 5.90 7.72 9.36 3.48 4.33 4.42 5.17 5.92 3.05 3.04 3.15 3.52 3.66

1.67 3.31 2.24 2.32 2.10 1.98 2.18 1.32 1.28 0.98 0.81 1.87 1.02 1.02 0.75 0.64

a

3.02 3.14 3.28 3.65

Using the 6-311++G** basis set. b Using the 6-311+G** basis

set.

Substitution Effect. The optimized geometries of the complexes of IBz with DB substituted with electron withdrawing groups are shown in Figure 4. The calculated SEs are presented in Table 2. It can be observed that there are drastic changes in the d values of the substituted complexes when compared to that for IBz · · · DB. Scrutiny of the results presented in Table 2 reveals that the substitution of DB by an electron withdrawing group increases the stability of the complexes in contrast to that of IBz · · · DB. Particularly, the substitution of DB by a cyano group considerably increases the stability of the complex. Furthermore, in the disubstituted categories, SEs of trans- and cis-substituted systems do not vary significantly and thus there

is no preference for one over the other in the formation of complexes. The SEs of cyano-substituted complexes range from 3.31 to 7.91 kcal/mol. Among all the systems, tetra-CN-DB has the highest SE of 7.91 kcal/mol. The SEs of complexes formed by the chlorine-substituted DB and IBz vary from 2.18 to 3.23 kcal/mol. The trend obtained for the chlorine-substituted systems are akin to that of cyano substitution of DB. The optimized geometries of complexes consisting of methylsubstituted DBs with IBz are shown in Figure 5. The d values of these complexes are less than that for IBz · · · DB. The calculated SEs for these complexes are listed in Table 2. The range in the SEs of these complexes denotes that the electron donating groups marginally increase the stability of the weak complexes. The overall trend in the substitution of electron donating group is akin to that of substitution by an electron withdrawing group. The plot between the SEs and the number of substituent groups present in the complex is given in the Supporting Information (Figure S4). It is found that SE increases with an increase in the number of substituent groups. Furthermore, it can be found that there is a linear relationship (in most of the cases R2 ) 0.99) between the number of substituents present in the complexes and the SEs. With a view to quantify the variations in the SEs with the number of substituent groups, the SE/substituent has been calculated. The SE/substituent is significantly more for the substitution of first group. Thereafter, the SE/substituent deceases. NBO Charges. The calculated NBO charges on the bridged H1 atom of DB and substituted DB in isolated and complexed states are presented in Table 3. The charges of bridged H atoms (H1 and H2) in isolated DB are similar. It can be seen from the results that the charge on the H1 atom (δ+) that is involved in the interaction with the π-cloud becomes more positive than in the isolated state. The substitution of nonbridge H atoms of DB by both electron withdrawing and donating groups increases the δ+ value on the H1 atom, which in turn enhances the binding affinities of substituted DBs with the IBz. The interaction

Figure 5. Optimized geometries of various complexes (DB containing various numbers of electron donating groups) selected in the present study with their corresponding bond lengths (in Å). Red, black, and blue numbers represent the values calculated from MP2/6-311++G**, M05-2X/6311++G**, and M05-2X/6-311+G** methods, respectively. [Here 3 corresponds to CH3 substitution and a, b, c, d, and e represent mono, 1,2-cis, 1,2-trans, tri, and tetra substitutions in each category.]

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TABLE 3: Calculated Charges on Bridged H-Atoms in the Isolated and Complexed States charge on Ha atom system

isolated molecule (H1 ) H2)

charge on H1a complex

charge on H2a

DB mono-CN-DB cis-di-CN-DB trans-di-CN-DB tri-CN-DB tetra-CN-DB mono-Cl-DB cis-di-Cl-DB trans-di-Cl-DB tri-Cl-DB tetra-Cl-DB mono-Me-DB Cis-di-Me-DB trans-di-Me-DB tri-Me-DB tetra-Me-DB

0.038 0.058 0.075 0.074 0.090 0.103 0.039 0.034 0.031 0.028 0.019 0.033 0.027 0.024 0.017 0.006

0.045 0.073 0.098 0.098 0.123 0.147 0.045 0.051 0.048 0.049 0.045 0.041 0.037 0.035 0.028 0.022

0.041 0.064 0.084 0.082 0.099 0.116 0.051 0.044 0.041 0.041 0.034 0.038 0.034 0.033 0.027 0.019

a

In (e-) units.

TABLE 4: Various Energy Components to the SEs (Electrostatic (Eelec), Exchange (Eexch), Induction (Eind), and Dispersion (Edis)) Obtained from DFT-SAPT Analysis complex

Eeleca

Eexcha

Einda

Edisa

Bz · · · DB IBz · · · DB IBz · · · mono-CN-DB IBz · · · cis-di-CN-DB IBz · · · trans-di-CN-DB IBz · · · mono-Cl-DB IBz · · · cis-di-Cl-DB IBz · · · trans-di-Cl-DB IBz · · · tri-Cl-DB IBz · · · mono-Me-DB IBz · · · cis-di-Me-DB IBz · · · trans-di-Me-DB

-5.267 -3.445 -5.598 -5.531 -7.124 -4.917 -4.816 -6.543 -8.020 -3.851 -2.942 -7.124

11.550 8.544 11.568 12.626 15.428 11.202 11.289 14.785 17.541 9.674 8.084 15.428

-0.127 0.031 -0.321 -1.212 -0.853 -0.076 -0.546 -0.283 -0.484 0.132 -0.183 -0.853

-6.680 -5.169 -6.813 -8.638 -8.747 -6.699 -7.992 -8.735 -10.270 -6.214 -6.896 -8.747

a

All the energies in kcal/mol.

between IBz and various DBs are governed by the interaction between δ+ of H1 atom of DBs and net π-electron cloud of IBz. Vibrational Analysis. The calculated vibrational frequencies of bridge B-H1-B and B-H2-B at the MP2/6-31G* level are reported in Table S2 of Supporting Information. B-H1-B and B-H2-B exhibit both asymmetric and symmetric stretching modes. It is evident from the analysis that in most of the cases a red shift occurs in the asymmetric stretching mode. The maximum red shift of 23 cm-1 is observed in the case of transdi-CN-DB and cis-di-Cl-DB. A minimum red shift value of 9 cm-1 is obtained for a weak H-bonded complex such as monoMe-DB. Further, tri-CN-DB shows a blue shift of 5 cm-1. There are no appreciable shifts in the symmetric stretching modes. Comparison of SEs. As mentioned in the previous sections, a series of new DFT methods have been developed with the view to develop suitable functions with wide applicability in chemistry and computational economy. The M05-2X method belongs to a similar category of density functional developed by Truhlar and co-workers.14 The SE values calculated from M05-2X methods are listed in Table 2. It can be found that values obtained from the M05-2X method are appreciably higher than MP2 results. The M05-2X results are also sensitive to the choice of basis set. The SEs values obtained from M05-2X/6311+G** are marginally higher than those calculated from

M05-2X/6-311++G**. A similar trend has also been reported by Truhlar and co-workers on a variety of weak H-bonded complexes.14c Calculated SEs at various levels of theories are in the Supporting Information (Table S3). The SEs obtained from CCSD(T)/6-31G* are marginally less than the MP2/631G* values. It is possible to note that there is a significant difference between the M05-2X and CCSD(T) values. DFT-SAPT Analysis. All the components of interaction energies, i.e., electrostatic (Eelec), exchange (Eexch), induction (Eind), and dispersion (Edis), are presented in Table 4 for some of the intermolecular complexes. The electrostatic and dispersive energy contributions to the stabilization of Bz · · · DB complex are -5.27 and -6.68 kcal/mol, respectively, whereas the same for the IBz · · · DB complex are -3.45 and -5.17 kcal/mol, respectively. It can be seen that both electrostatic and dispersion energy contributions are marginally higher for the Bz · · · DB complex than for IBz · · · DB. To gain insight into the role of dispersion vs electrostatic contributions, the ratios of dispersion and electrostatic energies (Edis/Eelec) have been compared. The ratios for the IBz · · · DB and Bz · · · DB are 1.49 and 1.27, respectively. These values indicate that Edis(IBz · · · DB) > Edis(Bz · · · DB). In the case of mono substitutions, the electron withdrawing group significantly influences the electrostatic contribution (Table 4). Typically, the electrostatic contribution to the stabilization of the IBz · · · mono-CN-DB, IBz · · · mono-Cl-DB, and IBz · · · mono-Me-DB complexes is -5.60, -4.92, and -3.85 kcal/mol, respectively. The corresponding dispersion contributions are -6.81, -6.70, and -6.21 kcal/mol. Similarly, in the case of disubstituted systems, the spatial position of the substituent exhibits the tremendous effect on the SE components. The electrostatic contributions to the IBz · · · cis-di-CN-DB and IBz · · · trans-di-CN-DB are -5.53 and -7.12 kcal/mol, respectively. Corresponding dispersion energy contributions are -8.64 and -8.75 kcal/mol. It can be seen that there is no significant difference in the dispersion energy component. A similar trend is found in the other substituted systems. The energy decomposition analysis reveals that both the electrostatic and dispersion contributions are linearly vary with the number of substituents. Overall, it can be noted that all these complexes are predominantly stabilized by the dispersive interaction. The values of Edis/Eelec elucidate the competitive role played by the electrostatic interaction in the stabilization of all the complexes. Conclusions In this study a systematic attempt has been made to calculate the structure, stability, and vibrational spectra of weak complexes formed by DB and IBz using various levels of theories. The calculated results have been compared with those values obtained for the complex formed between DB and Bz. It is found from the calculated geometrical parameters that DB forms a weak complex through the interaction of its bridge H atom with IBz. A similar interaction has also been observed for the Bz · · · DB complex. The typical difference between the IBz · · · DB and Bz · · · DB complexes can be noted from the MESP isosurfaces, which clearly explains the differences in the π-electron distributions of IBz and Bz rings. With a view to assess the changes in the SE upon substitution of the nonbridge H atom, both electron withdrawing and donating groups have been considered. It is found from the calculated geometrical parameters and SE values at the MP2/6-311++G** level that both the electron withdrawing and donating group favor the formation of weak complexes. The substitution by a cyano group significantly enhances the SE values. It is interesting to note

Interaction between Borazine and Diborane that the number of substituents present in the complex exhibits a linear relationship with the SEs. The calculated geometrical parameters and SE values have also been compared with the M05-2X level of calculations employing 6-311+G** and 6-311++G** basis sets. The overall trends obtained from MP2 and M05-2X calculations are similar. Furthermore, the scrutiny of SEs shows that MP2/6-31G* values are closer to the CCSD(T)/6-31G* results than the M05-2X values. The different parameters obtained from AIM analysis clearly indicate the weak interaction between the DB and IBz. The similarity in the interaction between DB and Bz can also be observed from these parameters. The interaction involving δ+ on the H1 atom of DB and the net π-electron cloud is also evident from the NBO charge analysis. The DFT-SAPT analysis reveals that the dispersion interaction primarily contributes to the SEs of all the complexes. Further, the same analysis elicits the competitive role played by the electrostatic interaction in the stabilization of various complexes. It is interesting to note from the DFT-SAPT analysis that Edis(IBz · · · DB) > Eelec(Bz · · · DB) and Eelec(IBz · · · DB) < Eelec(Bz · · · DB). The interplay of dispersion and electrostatic interactions in the stabilization of all the complexes is evident from the energy decomposition analysis. Acknowledgment. We are thankful to Prof. Shan Xi Tian and Hai-Bei Li (Hefei National Laboratory for Physical Sciences at Microscale, University of Science and Technology of China, China) for sharing his results on AIM calculations. P.R. thanks CSIR, New Delhi, India, for the award of Junior Research Fellowship. We thank R. Mahesh Kumar for his help in the DFT-SAPT calculations. We are grateful to E. R. A. Singam for his help in the preparation of the manuscript. Supporting Information Available: Systematic names of all substituted DB’s and all the abbreviations used in text, AIM topographies of all complexes, SE versus number of substituent plots, SEs values obtained at CCSD(T), MP2, and M05-2X employing 6-31G*, and IR-vibrational spectra of various complexes at MP2/6-31G*. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) (a) Pimentel, G. C.; Mc Clellan, A. L. The Hydrogen Bond; W. H. Freeman: San Francisco, CA, 1960. (b) Joesten, M. D.; Schaad, L. J. Hydrogen Bonding; Marcel Dekker: New York, 1974. (c) Jeffrey, G. A. An Introduction to Hydrogen Bonding; Oxford University Press: New York, 1997. (d) Scheiner, S. Hydrogen Bonding. A Theoretical PerspectiVe; Oxford University Press: Oxford, U.K., 1997. (e) Steiner, T. Angew. Chem., Int. Ed. Engl. 2002, 41, 48. (2) (a) Desiraju, G. R.; Steiner, T. The Weak Hydrogen Bond in Structural Chemistry and Biology; Oxford University Press: Oxford, U.K., 1999. (b) Desiraju, G. R. Acc. Chem. Res. 2002, 35, 565. (3) (a) Parthasarathi, R.; Subramanian, V.; Sathyamurthy, N. J. Phys. Chem. A 2006, 110, 3351. (b) Parthasarathi, R.; Subramanian, V. In Hydrogen Bonding: New Insights; Grabowski, S. J., Ed.; Challenges and Advances in Computational Chemistry and Physics 3; Kluwer: New York, 2006; p 1. (4) (a) Pauling, L. The Nature of the Chemical Bond; Cornell University Press: Ithaca, NY, 1939. (b) Basch, H.; Krauss, M.; Stevens, W. J. J. Am. Chem. Soc. 1985, 107, 7267. (c) Anwander, E. H. S.; Probst, M. M.; Rode, B. M. Biopolymers 1990, 29, 757. (d) Stone, A. J. Chem. Phys. Lett. 1993, 211, 101. (e) Burda, J. V.; Sponer, J.; Hobza, P. J. Phys. Chem. 1996, 100, 7250. (f) Sponer, J.; Burda, J. V.; Mejzly´k, P.; Leszczynski, J.; Hobza, P. J. Biomol. Struct. Dyn. 1997, 14, 613. (g) Burda, J. V.; Sponer, J.; Leszczynski, J.; Hobza, P. J. Phys. Chem. B 1997, 101, 9670. (h) Sponer, J.; Burda, J. V.; Sabat, M.; Leszczynski, J.; Hobza, P. J. Phys. Chem. A 1998, 102, 5951. (i) Sponer, J.; Sabat, M.; Burda, J. V.; Leszczynski, J.; Hobza, P. J. Biomol. Struct. Dyn. 1998, 16, 139. (j) Warshel, A. J. Biol. Chem. 1998, 273, 27035. (k) Tsuzuki, S.; Uchimaru, T.; Mikami, M. J. Phys. Chem. B 2009, 113, 5617.

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